Japanese Unexamined Patent Publication No. 2004-211708discloses an example of a compact piston pump utilized for a known oxygen concentrator or the like. The pump disclosed in Japanese Unexamined Patent Publication No. 2004-211708 is a two-headed reciprocating compressor having two cylinders. The pump includes: a motor having a drive shaft (motor shaft); two cylinders provided in a direction perpendicular to an axial direction of the drive shaft; and two pistons each having a piston head part and a rod part formed integrally, the piston head part fitting into a corresponding one of the two cylinders in a reciprocable fashion, and the rod part being rotatably installed to an eccentric shaft fixed to the motor shaft. In the two-headed reciprocating compressor, the piston head part of each of the two pistons makes intake-compression strokes in a compression chamber in the corresponding one of the cylinders, maintaining a 180-degree phase difference with each other.